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Theorem elndif 3714
 Description: A set does not belong to a class excluding it. (Contributed by NM, 27-Jun-1994.)
Assertion
Ref Expression
elndif (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))

Proof of Theorem elndif
StepHypRef Expression
1 eldifn 3713 . 2 (𝐴 ∈ (𝐶𝐵) → ¬ 𝐴𝐵)
21con2i 134 1 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1987   ∖ cdif 3553 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-dif 3559 This theorem is referenced by:  peano5  7039  extmptsuppeq  7267  undifixp  7891  ssfin4  9079  isf32lem3  9124  isf34lem4  9146  xrinfmss  12086  restntr  20899  cmpcld  21118  reconnlem2  22543  lebnumlem1  22673  i1fd  23361  dfon2lem6  31415  onsucconni  32099  meaiininclem  40023  caragendifcl  40051
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